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Quaternions are much easier to grasp once you are familiar with basic Lie group theory, in particular the adjoint representation of the group over its Lie algeb
by chombier 10y ago
Quaternions are much easier to grasp once you are familiar with basic Lie group theory, in particular the adjoint representation of the group over its Lie algebra.
Then the link with rotations becomes obvious and it gets very easy to transport geometric operations from the unit sphere to the rotation group (spherical linear interpolation, averaging, etc...)
- munchbunny 10y agoUnless I'm missing something, this feels like trying to understand a less complicated thing by first understanding a more complicated thing?
- chombier 10y agoSometimes this is the math way ;) More seriously, Lie group theory puts the light exactly on the shared structure between quaternions and rotations (both are smooth groups related in some way) and ignore the secondary details, so you spend time understanding what matters. It may be more abstract, but you get more from your efforts in my opinion.